Properties

Label 441.6
Level 441
Weight 6
Dimension 26583
Nonzero newspaces 20
Sturm bound 84672
Trace bound 3

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Defining parameters

Level: \( N \) = \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(84672\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(441))\).

Total New Old
Modular forms 35760 27020 8740
Cusp forms 34800 26583 8217
Eisenstein series 960 437 523

Trace form

\( 26583 q - 36 q^{2} - 72 q^{3} - 218 q^{4} + 93 q^{5} + 111 q^{6} + 62 q^{7} - 657 q^{8} - 474 q^{9} + O(q^{10}) \) \( 26583 q - 36 q^{2} - 72 q^{3} - 218 q^{4} + 93 q^{5} + 111 q^{6} + 62 q^{7} - 657 q^{8} - 474 q^{9} - 3201 q^{10} + 549 q^{11} + 2280 q^{12} - 191 q^{13} + 2166 q^{14} + 4440 q^{15} + 11802 q^{16} - 3729 q^{17} - 14112 q^{18} - 10817 q^{19} - 41607 q^{20} - 6894 q^{21} - 18714 q^{22} + 2577 q^{23} + 23529 q^{24} + 40404 q^{25} + 53841 q^{26} + 19992 q^{27} + 20214 q^{28} - 1773 q^{29} - 61056 q^{30} - 86615 q^{31} + 7062 q^{32} + 46368 q^{33} + 136290 q^{34} + 61233 q^{35} + 78783 q^{36} - 44931 q^{37} - 67404 q^{38} - 68808 q^{39} - 128883 q^{40} - 198999 q^{41} - 108246 q^{42} - 59503 q^{43} - 135993 q^{44} + 31362 q^{45} - 2985 q^{46} + 69927 q^{47} + 411279 q^{48} - 123042 q^{49} + 502851 q^{50} + 93360 q^{51} + 304031 q^{52} - 280347 q^{53} - 721467 q^{54} + 134430 q^{55} + 185412 q^{56} - 142902 q^{57} + 95181 q^{58} + 238359 q^{59} + 907092 q^{60} - 310894 q^{61} + 407349 q^{62} + 317532 q^{63} - 572927 q^{64} + 22131 q^{65} + 79962 q^{66} - 500799 q^{67} - 1179312 q^{68} - 671322 q^{69} + 591861 q^{70} + 532011 q^{71} - 671397 q^{72} + 1279009 q^{73} + 1018689 q^{74} + 194304 q^{75} + 733942 q^{76} + 166095 q^{77} + 1161738 q^{78} - 1217019 q^{79} - 2328138 q^{80} - 747138 q^{81} - 2376234 q^{82} - 1431675 q^{83} - 781668 q^{84} - 926577 q^{85} - 1526415 q^{86} - 1232268 q^{87} + 498057 q^{88} + 263751 q^{89} + 697044 q^{90} + 912377 q^{91} + 4806654 q^{92} + 2325378 q^{93} + 4003074 q^{94} + 3203181 q^{95} + 2734188 q^{96} + 505714 q^{97} - 2097708 q^{98} - 187872 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(441))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
441.6.a \(\chi_{441}(1, \cdot)\) 441.6.a.a 1 1
441.6.a.b 1
441.6.a.c 1
441.6.a.d 1
441.6.a.e 1
441.6.a.f 1
441.6.a.g 1
441.6.a.h 1
441.6.a.i 1
441.6.a.j 1
441.6.a.k 1
441.6.a.l 2
441.6.a.m 2
441.6.a.n 2
441.6.a.o 2
441.6.a.p 2
441.6.a.q 2
441.6.a.r 2
441.6.a.s 2
441.6.a.t 2
441.6.a.u 2
441.6.a.v 4
441.6.a.w 4
441.6.a.x 4
441.6.a.y 4
441.6.a.z 4
441.6.a.ba 6
441.6.a.bb 6
441.6.a.bc 6
441.6.a.bd 6
441.6.a.be 8
441.6.c \(\chi_{441}(440, \cdot)\) 441.6.c.a 4 1
441.6.c.b 24
441.6.c.c 40
441.6.e \(\chi_{441}(226, \cdot)\) n/a 162 2
441.6.f \(\chi_{441}(148, \cdot)\) n/a 400 2
441.6.g \(\chi_{441}(67, \cdot)\) n/a 392 2
441.6.h \(\chi_{441}(214, \cdot)\) n/a 392 2
441.6.i \(\chi_{441}(68, \cdot)\) n/a 392 2
441.6.o \(\chi_{441}(146, \cdot)\) n/a 392 2
441.6.p \(\chi_{441}(80, \cdot)\) n/a 132 2
441.6.s \(\chi_{441}(362, \cdot)\) n/a 392 2
441.6.u \(\chi_{441}(64, \cdot)\) n/a 690 6
441.6.w \(\chi_{441}(62, \cdot)\) n/a 552 6
441.6.y \(\chi_{441}(25, \cdot)\) n/a 3336 12
441.6.z \(\chi_{441}(4, \cdot)\) n/a 3336 12
441.6.ba \(\chi_{441}(22, \cdot)\) n/a 3336 12
441.6.bb \(\chi_{441}(37, \cdot)\) n/a 1392 12
441.6.bd \(\chi_{441}(47, \cdot)\) n/a 3336 12
441.6.bg \(\chi_{441}(17, \cdot)\) n/a 1128 12
441.6.bh \(\chi_{441}(20, \cdot)\) n/a 3336 12
441.6.bn \(\chi_{441}(5, \cdot)\) n/a 3336 12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(441))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(441)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)